The present invention relates to a digital coordinate measuring apparatus for determining surface coordinate values representing a model shape by scanning a model surface.
In the prior art, in a case where a complex three-dimensional shape is machined, a three-dimensional model thereof is made and machined using a profile milling machine. In recent years, however, machining is performed by a digital coordinate measuring apparatus which moves a scanning head relative to the model in a predetermined scanning plane while a stylus is contacted with the three-dimensional model surface and the magnitude of the displacement of the stylus is kept constant, and which samples coordinate data with respect to the trace of the spherical center of the stylus obtained by the position detecting apparatus. A numerical control (NC) machining apparatus controls the tools according to the sampled coordinate data. Such a digital coordinate measuring apparatus has come to be used for measuring the surface coordinate values of a model by calculating the coordinate value of a contact point between a stylus and the model.
In a conventional digital coordinate measuring apparatus, to determine contact points between a stylus and the model, the following equation (1) is used. ##EQU1## where G: position vector indicating the contact point between a stylus and a model
P: position vector indicating a machine coordinate value PA0 .epsilon.: displacement vector of the stylus PA0 R: radius of a spherical stylus
The above equation (1) will be explained with reference to FIG. 1. The vector .epsilon. and the vector -R.multidot..epsilon./.vertline..epsilon..vertline. actually overlap, but for the sake of understanding, they are depicted as being offset slightly in FIG. 1. Vector C is a position vector indicating the center of a stylus S, and is expressed by the following equation (2). EQU C=P+.epsilon. (2)
On the other hand, the position vector G indicating a contact point between a model M and the stylus S is expressed by the following equation (3), where the displacement vector .epsilon. of the stylus S is assumed to be a vector indicating the normal line direction of the model M. ##EQU2##
By eliminating the position vector C indicating the center of the stylus S from the above equations (2) and (3), the above equation (1) is derived.
As noted above, the displacement vector .epsilon. of the stylus S is assumed to be a vector indicating the normal line direction of the model M. Actually, however, the direction of the displacement vector .epsilon. of the stylus S deviates from the normal line direction of the model M due to friction between the model M and the stylus S. In FIG. 2, for example, it is known that the calculated position vector G indicating the contact point between the model M and the stylus S, which is determined from the above equation (1), deviates from the actual position vector G indicating the actual contact point between the model M and the stylus S. As a result, a problem arises in that an error occurs in the measurement value.